Applications of the diffusion decision model (DDM) to the study of cognitive individual differences consistently find that the model's drift rate (v) parameter forms a cohesive factor across many tasks and relates to measures of higher-order cognitive functioning, including general cognitive ability and working memory. This parameter is often interpreted as a measure of "processing speed," a traditional psychometric construct thought to reflect an individual's basic speed of information processing across tasks. However, conceptual differences between v and traditional notions of processing speed make this mapping far from straightforward. Racing accumulator models, which provide a more flexible and comprehensive account of behavioral data than the DDM, allow for the speed with which individuals accumulate evidence to be dissociated from the efficiency with which they accumulate task-relevant evidence (versus task-irrelevant evidence). We applied the DDM and a racing accumulator model to three tasks across three independent datasets to gauge the extent to which v parameter findings from the cognitive individual differences literature reflect speed of evidence accumulation (SEA) versus efficiency of evidence accumulation (EEA). Across all tasks, v was more strongly related to EEA than SEA. EEA was consistently related to measures of general cognitive ability, working memory, and executive function whereas SEA explained <1% of the variance in each. These findings suggest individual differences in the DDM's v parameter, and its relations with higher-order cognitive abilities, primarily reflect EEA rather than SEA and challenge the widespread practice of equating v with the traditional "processing speed" construct.

EMC2 is an R package that provides a comprehensive five-phase workflow for Bayesian hierarchical analysis of cognitive models of choice. In the design phase, EMC2 bridges the gap between standard regression analyses and cognitive modeling through linear-model specifications for cognitive-model parameters. In the Bayesian specification and sampling phases, the package provides flexible priors, hierarchical structures, and efficient sampling algorithms, enabling fast, user-friendly estimation of computationally intensive cognitive models. In the final two phases, EMC2 provides a suite of functions for model criticism and inference. Using two leading evidence-accumulation models for illustration, we provide a tutorial on the EMC2-based workflow that eases and guides the process of specifying, evaluating, refining, comparing, and interpreting Bayesian hierarchical cognitive models.

Biased information processing plays an important role in mental disorders. This study investigates choice biases in value-based decision making and how links to psychological resilience are related to individual differences in cognitive and neural processing of reward and punishment signals. In a cost-benefit integration task, 82 participants (41 female, 41 male human subjects) weighed gains and losses associated with different features (color, shape) of compound visual stimuli. A positive choice bias in decision making was associated with trait acceptance as a facet of self-reported resilience-and this cross-sectional link was statistically mediated by differences in the neural processing of value information as measured with fMRI: Participants with a more positive choice bias and higher trait acceptance showed stronger increases in neural activity in response to negative information (loss) in 10 prefrontal and parietal brain regions-and stronger decreases in response to positive information (gain) in the right inferior frontal junction. Cognitive-computational modeling revealed that more positive choice biases were associated with lower sensitivity to and valuation of negative relative to positive information. Notably, higher valuation of positive information was associated with stronger neural responses to negative information in dACC and insula. Finally, choice bias and trait acceptance were associated with functional connectivity between prefrontal seeds, midbrain, striatum, and ventromedial prefrontal cortex. The stronger activation of brain regions associated with cognitive control, specifically for negative information, suggests a stronger regulatory influence on the processing of negative information, potentially promoting a positive choice bias that is able to support resilience.

In tasks such as the Simon, Stroop, and Flanker, different attributes of a choice stimulus can be associated with conflicting responses. These tasks have been widely used to afford insights about cognitive control by comparing performance when the attributes are congruent vs. incongruent. It is usually assumed that standard evidence-accumulation models (EAMs), which were originally developed to explain simple choices about non-conflict stimuli, cannot accommodate the fine-grained effects of congruency on the speed and accuracy of responses in conflict tasks. We investigated this assumption by fitting data from over 500 subjects performing each of these three conflict tasks using five types of standard EAMs drawn from two classes, race and dual-diffusion models. For each type, we fit a range of variants that explain conflict effects using one or more parameter differences. We found that the two dual-diffusion models could not accommodate the fine-grained effects of congruency, but the three race models could. All the race models explain the congruency effects in the same way, with mechanisms that affect the amount of evidence required to decide, and the variability of that evidence. We discuss how this combination of mechanisms suggests a novel “conflict-cancelation” theory of cognitive control.

This tutorial presents a comprehensive framework for modelling structured trial- by-trial variability in evidence accumulation models (EAMs). Traditional EAMs assume independent and identically distributed (IID) parameters across tri- als, which fails to capture the temporal dynamics and structured variability inherent in cognitive processes. We introduce Bayesian hierarchical methods to estimate EAMs that incorporate trial-level variability, offering both data- driven and theory-driven approaches. Data-driven methods describe how decision processes vary across trials using trend models, while theory-driven methods explain adaptations in response to specific factors. By moving beyond the IID assumption, our approach allows for a more precise characterisation of dynamic cognitive processes such as learning, adaptation, and fatigue. This tutorial pro- vides step-by-step guidance on implementing these methods using the EMC2 package, demonstrating their application to experimental paradigms involving choice and response time data.

Models of human sensorimotor control have been developed from two perspectives. The human performance modelling perspective relies on mathematically complex models that cover a wide range of perceptual, decision and motor processes to understand human-machine interactions in complicated, realistic settings. The fundamental research perspective relies on mathematically tractable models to understand physical and statistical aspects of sensorimotor control in simple laboratory settings. In the present work we combine the two perspectives to develop a Stochastic Delay Differential Equation (SDDE) model of driving performance while multitasking. Our model comprises of three psychologically interpretable parameters that quantify cognitive sensitivity, delays, and noise. We apply our model to time-series data from a two-dimensional compensatory tracking task that simulates lateral and longitudinal control of a ground vehicle. Concurrently with the primary tracking task, participants performed secondary tasks that required mainly cognitive resources, or greater visual-manual resources. We show how our model can provide more fine-grained insight into the mechanisms underlying driver distraction than conventional one-dimensional behavioural measures.

A major target for evidence accumulation models of decision-making has been the development of a joint account of confidence, accuracy, and latency. While successful extensions to confidence have been made, there remains a lack of consensus as to how confidence is generated and there have been few comparisons between existing models. In this work, we developed and compare three different mechanisms for confidence generation in the linear ballistic accumulator framework (S. D. Brown &amp; Heathcote, 2008). These take the form of a.) multi-alternative decisions among all of the confidence options as a competitive race, b.) the balance of evidence between the response alternatives (the multiple threshold race; Reynolds et al., in revision), and c.) confidence being inversely proportional to the amount of subjective time that has elapsed in the decision, which is measured as a separate accumulation process. Each theory was tested against two experiments that manipulated the number of confidence options in a decision (Experiment 1) or the amount of time pressure (Experiment 2). All theories cleared the empirical hurdles, but there were also subtle differences between each of the theories in their ability to address the data: although all models showed generally adequate parameter recovery, the Confidence Accumulator failed to produce theoretically sensible parameter shifts across confidence-scale conditions whereas the Timing theory was unable to address fast low-confidence patterns in individual participants; meanwhile, both the MTR and the Timing theory had questionable plausibility in addressing the double-increase pattern of confidence.

Experimental manipulations in conflict tasks, e.g., the Stroop, Flanker, and Simon tasks, lead to systematically poorer performance in “incongruent” conditions that feature stimuli that contradict task goals. However, substantial recent debate surrounds whether individual differences in conflict task behavior reflect reliable, trait-like mechanistic processes. Much prior work uses difference scores, contrasting performance between incongruent and congruent trials to index conflict suppression ability, but recent work demonstrates these scores exhibit poor psychometric properties. Formal cognitive process models suggest that individual differences in conflict suppression are driven by task-general processes, as opposed to processes specialized for conflict. However, this prior work separately models cognitive process parameters and their covariation, which fails to adequately account for measurement error. Here, we model distinct mechanisms of conflict task performance and their covariance simultaneously using hierarchical Bayesian joint modeling methods for the first time which improves individual estimation and accounts for error. We fit the conflict linear ballistic accumulator model (LBA) to two large datasets containing multiple conflict tasks and test-retest sessions, and an additional large dataset containing a conflict task and simple perceptual decision-making task. First, within conflict tasks, we found moderate test-retest reliability for both conflict-specific processing mechanisms, and, to a larger degree, task-general mechanisms. Second, task-general, but not conflict-specific, mechanisms were correlated across different conflict tasks. Third, these task-general mechanisms were correlated between conflict tasks and a simple decision-making task without conflict suppression demands. Overall, we found robust individual differences in computational mechanisms underlying general decision-making, but not mechanisms specific to conflict processing.

Cognitive models, such as evidence-accumulation models, are increasingly used in individual differences research in psychology and neuroscience. By computing correlations between cognitive model parameters across participants, researchers aim to understand how the psychological processes the parameters represent relate to one another and jointly determine performance. It is generally acknowledged that cognitive models can be challenging to estimate due to strong within-subject correlations among the parameters, which are embedded in the model’s likelihood function. What is less often recognized, however, is that within-subject correlations can also distort correlations computed between parameters estimated with non-hierarchical methods, so they no longer reflect true individual differences, potentially leading to misleading conclusions. Here we illustrate this pitfall of non-hierarchical estimation and show how appropriately parameterized hierarchical models can mitigate the problem by effectively separating within- and between-subject sources of variation. We then offer recommendations for identifying and guarding against the inferential biases resulting from the strong within-subject correlations inherent in many cognitive models.

Race models describe speeded decision-making as a race between competing runners that accumulate evidence in favor of available choice options. Their parameters can be estimated through the model likelihood that combines the probability and cumulative density functions of each runner. However, estimating parameters of complex race models whose runners have intractable densities with (hierarchical) Bayesian inference has been challenging: Numerical density approximations tend to be slow and amortized neural posterior estimation methods require complex network architectures that can be expensive to train and, in classical settings, tie the trained estimator to a specific prior distribution and generative model. We propose a flexible neural estimation method that decouples training from the choice of prior distribution or model parameterization. We train a small neural network together with a monotonic neural spline flow to simultaneously learn the runners' conditional probability density and cumulative density functions. We then combine both functions to efficiently estimate race model likelihoods that can be used in combination with modern samplers. We demonstrate the utility of our approach on both tractable and intractable versions of the popular racing diffusion model. Based on our results, we argue that, when flexibility in choosing prior distributions or model parameterizations is needed, learning the model likelihood with lightweight neural density estimators is advantageous.

Response times (RTs) are crucial in experimental psychology, providing insights into affective and cognitive processes. Although the finite resolution of stimulus presentation and response recording introduce noise into measured RTs, methods used to fit RT-based cognitive models typically ignore this source of measurement uncertainty. We mathematically characterize the effects of different types of measurement error on RT distributions. We then investigate how a range of realistic levels of measurement noise affect the estimation of five prominent evidence-accumulation models of RT and choice. Although models differ in sensitivity, we find that in all cases the estimation of at least some parameters is distorted by realistic levels of measurement noise. We propose and evaluate a ``binning'' method that not only ameliorates the resulting biases, but can also substantially reduce the computational cost of model fitting.

Evidence accumulation models (EAMs) explain and predict human choices and response times in a way that maps more directly to cognitive processes than traditional analyses. For example, EAMs can separate the speed-accuracy trade-off from processing capacity. However, little guidance is available regarding how to use EAMs to instantiate cognitive process theories, which often involve complex mappings of parameters to experimental designs. This tutorial illustrates how to embed such theories using the R package EMC2. We show how the effects of cognitive processes can be estimated by mapping EAM parameters to experimental designs using an augmented linear model language. We demonstrate with two examples. The first instantiates a theory of prospective memory. The second instantiates a theory of how humans integrate advice from automated decision aids into their choices. We then show how to combine these two different theories in a unified framework. We conclude by discussing further directions for theory embedding, including non-linear mappings from stimulus values to EAM parameters and the incorporation of trial-by-trial dynamics.

There is a growing realization that experimental tasks that produce reliable effects in group comparisons can simultaneously provide unreliable assessments of individual differences. Proposed solutions to this “reliability paradox” range from collecting more test trials to modifying the tasks and/or the way in which effects are measured from these tasks. Here, we systematically compare two proposed modeling solutions in a cognitive conflict task. Using the ratio of individual variability of the conflict effect (i.e., signal) and the trial-by-trial variation in the data (i.e., noise) obtained from Bayesian hierarchical modeling, we examine whether improving statistical modeling may improve the reliability of individual differences assessment in four Stroop datasets. The proposed improvements are (1) increasing the descriptive adequacy of the statistical models from which conflict effects are derived, and (2) using psychologically motivated measures from cognitive measurement models. Our results show that the type of model does not have a consistent effect on the signal-to-noise ratio: the proposed solutions improved reliability in only one of the four datasets. We provide analytical and simulation-based approaches to compute the signal-to-noise ratio for a range of models of varying sophistication and discuss their potential to aid in developing and comparing new measurement solutions to the reliability paradox.

This study examines how individuals adapt to varying levels of prospective memory (PM) and ongoing-task difficulty in a cognitively demanding task environment. PM – the ability to remember and execute delayed intentions while engaged in other tasks – depends on flexible allocation of limited-capacity cognitive resources and strategic cognitive control. Prior research has rarely manipulated both PM and ongoing-task difficulty within the same study, has typically used relatively undemanding tasks that unlikely exceed human capacity to manage them, and has often relied on aggregate performance measures that cannot disentangle capacity sharing from cognitive control. To address these limitations, we orthogonally manipulated PM and ongoing-task difficulty within subjects using a demanding air-traffic control task and applied Prospective Memory Decision Control – a cognitive process model that jointly quantifies individuals’ capacity allocation and cognitive control strategies. As PM difficulty increased, participants reallocated cognitive capacity from the ongoing task to the PM task and adopted a cognitive control strategy that favoured PM: raising decision thresholds for ongoing responses and lowering them for PM responses. By contrast, increased ongoing-task difficulty impaired information processing quality for both tasks (i.e., reduced signal-to-noise ratio) and led participants to lower PM thresholds without changing thresholds for the ongoing task. These findings provide model-based evidence consistent with distinct contributions of capacity sharing and cognitive control within the PMDC framework and illustrate the value of formal modelling in a demanding PM setting.

Biased information processing plays an important role in mental disorders. This study investigates choice biases in value-based decision making and how links to psychological resilience can be accounted for by individual differences in cognitive and neural processing of reward and punishment signals. In a cost-benefit integration task, 82 participants (41 female, 41 male human subjects) weighed gains and losses associated with different features (color, shape) of compound visual stimuli. A positive choice bias in decision making was associated with trait acceptance as a facet of self-reported resilience – and this association was mediated by differences in the neural processing of value information as measured with fMRI: Participants with a more positive choice bias and higher trait acceptance showed stronger increases in neural activity in response to negative information (loss) in ten prefrontal and parietal brain regions – and stronger decreases in response to positive information (gain) in the right inferior frontal junction. Cognitive-computational modeling revealed that more positive choice biases were associated with lower sensitivity to and valuation of negative relative to positive information. Notably, higher valuation of positive information was associated with stronger neural responses to negative information in dACC and insula. Finally, choice bias and trait acceptance were associated with functional connectivity between prefrontal seeds, midbrain, striatum, and ventromedial prefrontal cortex. The stronger activation of brain regions associated with cognitive control, specifically in response to negative information, may reflect a stronger regulatory influence on the processing of negative information, potentially promoting a positive choice bias that supports resilience.

There are many well-studied models for preference, such as Luce's choice model and other random utility accounts. More recently, there has been some interest in extending preference models to also account for decision times. We identify a limit to this extension, by noting a correspondence between preference models and theories of simple, rapid decision-making (response time models). Some preference models are known to predict "separable" choices and response times. This mathematical property has been extensively studied - empirically and theoretically - for simple decision-making. In that context, there are well-known and robust empirical phenomena describing predictable differences between the speeds of different response choices. This link provides insight into the interpretability of some random utility models as response time models, and also constraints on the development of theories of preference.

Evidence accumulation models (EAMs) are popular tools for explaining speeded decisions because their parameters capture different aspects of the decision process. While researchers increasingly use Bayesian methods for estimating EAM parameters, computational costs and the necessity of tractable model likelihoods still pose obstacles for traditional methods such as Markov chain Monte Carlo (MCMC). Neural posterior estimation (NPE) addresses these obstacles by training a neural network to approximate the joint posterior distribution from simulated data, which only requires a generative model and amortizes computational costs at inference time. However, the quality of the approximation can suffer when the test data at inference time differs from the training data. Both test and training data stem from data-generating contexts and, for EAMs, these are influenced by the experimental design. Using the Racing Diffusion Model as a test case, we investigated how well NPE can generalize across changes in two types of experimental design contexts: number of trials and data-generating prior contexts that affect the error rate. Using MCMC as a reference, we showed in two simulation studies that NPE generalized well across changes in trial numbers but less well across error rates. We applied NPE to empirical datasets from reasoning tasks and found that the patterns observed in our simulation studies held. We discuss challenges and future directions to assess and improve the generalization for neural estimators for EAMs.

Research into cognitive control has flourished over the last three decades across many areas of the psychological and neural sciences, but problems have recently emerged that raise foundational questions about what cognitive control is, how individual differences should be measured, and the validity of cognitive control as an explanation for variation in behavioral traits and clinical conditions. Here, we outline a novel perspective that is rooted in evidence accumulation models, formal mathematical models that explain how individuals make choices across many contexts. We review model-based work that distinguishes conflict-specific processes, which are selectively engaged to address goal-conflicting information, from task-general processes that facilitate goal-congruent responding irrespective of the presence of conflict. We then highlight the computationally-derived measure we call efficiency of evidence accumulation (EEA) that reflects the task-general amplification of goal-congruent information. EEA forms a trait-like individual difference dimension, explains individual differences in performance in cognitive control tasks, and shows clear relevance to behavioral traits and clinical conditions in which control is thought to be impaired. These findings help address multiple theoretical, methodological, and empirical challenges in the study of cognitive control and provide a promising way forward for characterizing control processes that enhance goal-relevant responding across time and contexts.

Event-Based Prospective Memory (PM) requires performing a planned action upon encountering a target event. The PM decision control (PMDC) model quantifies the dual mechanisms of cognitive control (proactive and reactive, Braver, 2012) that support PM. Here, we test a key prediction of the dual-mechanisms theory: that cognitive control will shift from proactive to reactive as the need for control lessens due to PM targets being infrequent. Participants made lexical decisions (ongoing task) and were presented blocks of trials which either contained no PM targets, a high PM target frequency (19% of trials), or a low PM target frequency (5%). We fit the behavioural data with an extended version of PMDC that was augmented to specify the ongoing-task habituation and PM learning dynamics required to account for the way in which participants adapted their behaviour as a function of task practice and expected PM target frequency. PM costs (ongoing task response slowing in PM conditions relative to no PM target condition) were observed only in the high frequency condition, explained by PMDC by an increase in proactive control. PM accuracy was similar across high and low frequency conditions early in the experiment, but later an advantage emerged for the lower frequency PM task. PMDC accounted for this with stronger reactive control in low frequency condition that increased over practice. Our results confirm the prediction that control shifts from proactive to reactive with lower target event frequency, respond to recent calls from the PM literature for theory to account for across-trial dynamics.

Biased information processing plays an important role in mental disorders. This study investi-gates biases in value-based decision making and how links to psychological resilience can be accounted for by individual differences in the cognitive and neural processing of affective in-formation. Decision making was studied in 82 people (41 female, 41 male; age: 18–37 years) using a cost-benefit integration task. Neural activity was recorded via fMRI, cognitive pro-cessing modeled with an evidence-accumulation model. Choice bias was positively associated with self-reported resilience (particularly the facet ‘acceptance’) – and this association was me-diated by differences in the neural processing of affective information during decision making: Participants with a more positive bias and higher resilience showed stronger increases in neural activity in response to loss in ten prefrontal and parietal brain regions – and stronger decreases in response to gain in the right inferior frontal junction. Cognitive-computational modeling re-vealed that more positive biases were associated with lower sensitivity to and lower valuation of negative information – along with relatively higher sensitivity to and higher valuation of positive information. Notably, higher valuation of positive information was associated with stronger neural responses to negative information in dACC and bilateral insula. Finally, bias and resili-ence were associated with differential functional connectivity between prefrontal seeds, midbrain, striatum, and ventromedial prefrontal cortex. The findings suggest that stronger activation of brain regions associated with cognitive control – specifically in response to negative information – promotes a positive cognitive bias in affective decision making that may support resilience to mental disorders.